Roots of crosscap slides and crosscap transpositions
نویسندگان
چکیده
منابع مشابه
Crosscap Numbers of Two-component Links
We define the crosscap number of a 2-component link as the minimum of the first Betti numbers of connected, nonorientable surfaces bounding the link. We discuss some properties of the crosscap numbers of 2-component links.
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We define the concordance crosscap number of a knot as the minimum crosscap number among all the knots concordant to the knot. The four-dimensional crosscap number is the minimum first Betti number of non-orientable surfaces smoothly embedded in 4-dimensional ball, bounding the knot. Clearly the 4-dimensional crosscap number is smaller than or equal to the concordance crosscap number. We constr...
متن کاملOff - shell Crosscap State and Orientifold Planes
We show that a non-trivial dilaton condensation alters the dimensions of orientifold planes. An off-shell crosscap state which naturally interpolates between the usual onshell crosscap states and their T-duals plays an important role in the analysis. We present an explicit representation of the off-shell crosscap state on an RP 2 worldsheet in the gauge in which the worldsheet curvature in the ...
متن کاملCrosscap States for Orientifolds of Euclidean AdS3
We propose the crosscap states for orientifolds of Euclidean AdS3. We show that our crosscap states reproduce the geometry of orientifolds, which is AdS2. The spectral density of open strings in the system with orientifold can be read from the Möbius strip amplitudes and is compared to that of the open strings stretched between branes and their mirrors. We also compute the Klein bottle amplitud...
متن کاملBounds on the Crosscap Number of Torus Knots
For a torus knot K, we bound the crosscap number c(K) in terms of the genus g(K) and crossing number n(K): c(K) ≤ ⌊(g(K) + 9)/6⌋ and c(K) ≤ ⌊(n(K)+16)/12⌋. The (6n− 2, 3) torus knots show that these bounds are sharp.
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ژورنال
عنوان ژورنال: Periodica Mathematica Hungarica
سال: 2017
ISSN: 0031-5303,1588-2829
DOI: 10.1007/s10998-017-0210-3